Related papers: An information upper bound for probability sensiti…
The aim of this work is to provide bounds connecting two probability measures of the same event using R\'enyi $\alpha$-Divergences and Sibson's $\alpha$-Mutual Information, a generalization of respectively the Kullback-Leibler Divergence…
Noise affects the performance of quantum technologies, hence the importance of elaborating operative figures of merit that can capture its impact in exact terms. In quantum metrology, the introduction of the Fisher information measurement…
The predictability of a time series is determined by the sensitivity to initial conditions of its data generating process. In this paper our goal is to characterize this sensitivity from a finite sample by assuming few hypotheses on the…
The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we…
We establish analogs of Cheeger's inequality for probability measures with heavy tails. As one of the principal applications, suppose $\lambda > 3$ and define the (Pareto) probability measure $\mu_{\lambda}$ on $[1,\infty)$ by…
This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, are also used in many…
We derive tight and computable bounds on the bias of statistical estimators, or more generally of quantities of interest, when evaluated on a baseline model P rather than on the typically unknown true model Q. Our proposed method combines…
Studying the effects of one-way variation of any number of parameters on any number of output probabilities quickly becomes infeasible in practice, especially if various evidence profiles are to be taken into consideration. To provide for…
The two principal/immediate influences -- which we seek to interrelate here -- upon the undertaking of this study are papers of Zyczkowski and Slomczy\'nski (J. Phys. A 34, 6689 [2001]) and of Petz and Sudar (J. Math. Phys. 37, 2262…
Uncertainty quantification is a primary challenge for reliable modeling and simulation of complex stochastic dynamics. Such problems are typically plagued with incomplete information that may enter as uncertainty in the model parameters, or…
The Fisher Information matrix is a widely used measure for applications ranging from statistical inference, information geometry, experiment design, to the study of criticality in biological systems. Yet there is no commonly accepted…
Probabilistic sensitivity analysis identifies the influential uncertain input to guide decision-making. We propose a general sensitivity framework with respect to the input distribution parameters that unifies a wide range of sensitivity…
We derive independence tests by means of dependence measures thresholding in a semiparametric context. Precisely, estimates of phi-mutual informations, associated to phi-divergences between a joint distribution and the product distribution…
Sensitivity analysis of a numerical model, for instance simulating physical phenomena, is useful to quantify the influence of the inputs on the model responses. This paper proposes a new sensitivity index, based upon the modification of the…
Bayesian model averaging is a practical method for dealing with uncertainty due to model specification. Use of this technique requires the estimation of model probability weights. In this work, we revisit the derivation of estimators for…
We propose and discuss sensitivity metrics for reliability analysis, which are based on the value of information. These metrics are easier to interpret than other existing sensitivity metrics in the context of a specific decision and they…
Quantum Fisher information places the fundamental limit to the accuracy of estimating an unknown parameter. Here we shall provide the quantum Fisher information an operational meaning: a mixed state can be so prepared that a given…
Bayesian networks are one of the most widely used classes of probabilistic models for risk management and decision support because of their interpretability and flexibility in including heterogeneous pieces of information. In any applied…
Fisher information, lies at the heart of parameter estimation theory, was recently found to have a close relation with multipartite entanglement (Pezz\'{e} and Smerzi, Phys. Rev. Lett. 102, 100401). We use Fisher information to distinguish…
The Fisher information metric or the Fisher-Rao metric corresponds to a natural Riemannian metric defined on a parameterized family of probability density functions. As in the case of Riemannian geometry, we can define a distance in terms…